Your constitutional right to free speech protects you from government censorship or punishment but generally does not protect speech rights against private employers, who can regulate or discipline employee speech.
Your constitutional right to free speech does not extend to your employer . You have the right to say all the stupid , heinous evil shit you want and you're protected from government prosecution, imprisonment or worse.

What free speech rights do government employees have? - The Foundation for Individual Rights and Expression
Source: thefire.org
Key Evidence
Multiple sources confirm that the First Amendment protects against government interference but does not guarantee free speech rights in private employment settings.
thefire.orgthefire.orgWhat free speech rights do government employees have?
forbes.comforbes.comYour Free Speech Rights (Mostly) Don't Apply At Work+1 more
Public employees have limited free speech protections when speaking on public matters, subject to balancing tests.
firstamendment.mtsu.edufirstamendment.mtsu.eduPublic Employees
houstonlawreview.orghoustonlawreview.orgThe Free Speech of Public Employees at a Time of Political Polarization:...
Employers can lawfully limit employee speech to maintain workplace order and protect business interests.
fisherphillips.comfisherphillips.comSpeak No Evil – The Right To Limit Employee Speech This Election Season And...
welcometothejungle.comwelcometothejungle.comFree speech at work? Usually not, but here are 7 exceptions
What the Evidence Shows
The First Amendment of the U.S. Constitution primarily restricts government actions and protects individuals from government censorship or punishment for their speech. This means that when you speak, you are protected from government prosecution, imprisonment, or other penalties for your expression, even if the speech is offensive or hateful.
However, this protection does not extend to private employers. Private companies have the legal right to regulate employee speech within the workplace and can discipline or terminate employees for speech they find objectionable or disruptive. Public employees (those working for government entities) have some First Amendment protections when speaking on matters of public concern, but these rights are balanced against the government's interest in maintaining an efficient and disruption-free workplace (Pickering balancing test).
Even public employees' speech rights are not absolute and can be limited under certain circumstances. Therefore, while you can say almost anything without fear of government punishment, your employer, if private, can impose restrictions and consequences on your speech at work.